"Organic farming" refers to a particular way of producing foods and fibers. Organic farming is applying that way of producing food specifically to growing crops that have not been genetically altered and have not been grown using any synthetics. Organic farming is often considered the most "natural" way to farm in the sense that it relies solely on nature-made fertilizers (namely manure) and no man-made pesticides. About two percent of the United States food supply is currently grown organically.
Farmers can be considered to be growing "certified organic" crops by meeting national standards, including a system plan for growing the crops, proper buffer fields between the organic field and any non-organic fields (preventing non-organic pollen from fertilizing organic crops) and much record keeping of crop information. All crops that are to be sold as organic must be certified.
One common misconception is that organic and natural crops are the same thing. A crop is natural if it is not genetically modified; it may still have been grown using synthetic pesticides and fertilizers. Organic crops are free from anything synthetic.
For more information, here are some websites Mitch found in his research. Be sure to use your critical thinking skills as you read them.